Algebra Find each missing angle measure.

See Problem 3.

20. A ramp forms the angles shown below. What are the values of a and b?

    

21. A lounge chair has different settings that change the angles formed by its parts. Suppose m ∠ 2 = 71 m angle , 2 equals 71  and m ∠ 3 = 43 . m angle . 3 equals 43 .  Find m ∠ 1 . m angle 1 .

B Apply

Algebra Use the given information to find the unknown angle measures in the triangle.

22. The ratio of the angle measures of the acute angles in a right triangle is 1 : 2.
23. The measure of one angle of a triangle is 40. The measures of the other two angles are in a ratio of 3 : 4.
24. The measure of one angle of a triangle is 108. The measures of the other two angles are in a ratio of 1 : 5.
25. Think About a Plan The angle measures of Δ RST cap delta  are represented by 2x, x + 14 , x plus 14 comma  and x − 38 . x minus 38 .  What are the angle measures of Δ RST ? cap delta
    • How can you use the Triangle Angle-Sum Theorem to write an equation?
    • How can you check your answer?

26. Proof Prove the following theorem: The acute angles of a right triangle are complementary.

    Given: Δ ABC cap delta  with right angle C

    Prove: ∠ A angle eh  and ∠ B angle b  are complementary.

    

27. Reasoning What is the measure of each angle of an equiangular triangle? Explain.

28. Draw a Diagram Which diagram below correctly represents the following description? Explain your reasoning.

    Draw any triangle. Label it Δ ABC . cap delta  Extend two sides of the triangle to form two exterior angles at vertex A.

    1. 
    2. 
    3. 

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